Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n = int(input())


def triangular_number(k):
    return int(k*(k+1)/2)

found = False
for i in range(1, n):
    a = triangular_number(i)
    b = n - a
    try:
        found = int((2*b + 0.25)**0.5 - 0.5) == (2*b + 0.25)**0.5 - 0.5 and int((2*b + 0.25)**0.5 - 0.5) > 0
    except:
        found = False
        break
    if found:
        print("YES")
        break
if not found:
    print("NO")